Tangency portfolio and Capital Market Line

What happens when a riskless asset is added to the model? If and X is any risky portfolio, then and obviously, . This means that those portfolios form a straight line on the mean-standard deviation plane. Any portfolio on this line is available by investing into R and X. It is clear that the best choice for X is the point where this line is tangent to Efficient Frontier. This tangency point is called the market portfolio or tangency portfolio, and the tangent of Efficient Frontier of risky assets at this point is called Capital Market Line (CML), which consists of the efficient portfolios of all the assets in this case. The last question that we address regarding the mean-variance model is how the market portfolio (or equivalently, the CML) can be determined.

We can easily modify the variance minimization code to accomplish this. First of all, if we add a riskless asset, a full-zero row and column is added to the covariance matrix (where n is...